Mixing structures and characteristics are crucial to the mixing quality of spherical/cylindrical binary granular systems like the biomass-coal mixtures which can affect energy release and carbon emissions. In this work, the mixing of binary spheres/cylinders in a rotating drum was numerically reproduced by using discrete element method (DEM). Systematic parametric studies were conducted to identify the role of various parameters such as rotation speed (ω) of the drum, aspect ratio (AR), mass fraction (φ_c) and volume fraction (φ_v) of cylindrical particles, and the density difference (φ_ρ) between the binary particles; meanwhile, corresponding mechanisms were also explored by analyzing the kinetic energy. Results show that when the flow regime is rolling/cascading, the mixing quality can be effectively improved; however, when the flow regime is cataracting, the mixing quality becomes worse. With AR close to 1.0, the interlocking effect between particles becomes weaker and the porosity becomes smaller, which leads to the higher contact efficiency and thus improves the mixing quality. Binary mixtures with different φ_c are synergistically affected by energy input and interlocking structure. The volume of spherical particles is more conducive to improving the mixing quality than that of cylindrical particles when the volume of the granular system is at the same level. The φ_ρ can cause segregation behavior of particles so as to make the mixing quality worse.

A coupled approach of discrete element method and pore network model (DEM-PNM) is developed for simulating particle–fluid flow. By this approach, the particle/solid flow is described at a particle scale by DEM and the fluid flow is described at a pore scale by PNM. The coupling scheme between DEM and PNM and the boundary conditions for realizing particle–fluid flows under different conditions are explicitly introduced. The capability is examined in three systems: a dynamic cell, a gas-fluidized bed, and a packed bed with lateral gas injection. The simulated results by the DEM-PNM approach agree with those results by either DEM-LBM (lattice Boltzmann method) approach or experiments. In particular, the simulated reasonable flow patterns in gas fluidization and lateral gas injection demonstrate the applicability of the proposed approach to complex particle–fluid flow. However, the current model presents less accuracy in dilute flow region and does not consider some important factors, which should be further improved in the future.

The densification of mono-sized regular octahedral particles under vibration is simulated by a DEM model. The model is validated by physical experiments. The effects of operating parameters including vibration amplitude and frequency are investigated. The obtained packing structures are characterized, and corresponding densification mechanisms are identified. The results indicate that vibration amplitude is more critical for densification compared to frequency, where a wide range of suitable amplitudes exists to realize the dense packing structures. Ordered packing structure exists in boundary region. The central region possesses good particle position randomness and orientation randomness, and the packing density for poured packing (initial loose packing) and vibrated packing (dense packing) in the central region are 0.670 and 0.684, respectively. During densification, contacts and constraints between particles decrease, and the stress within the structure becomes larger. The typical arrangement of neighboring particles is close to but not perfect face to face (F–F) contact. Particles in the boundary region experience more rotations and can form local ordered structures. These structures prevent the relative movement of individual particles but favor their movement as a whole. Particles in the central region have relatively little movement and rotation. The ordered structures formed at boundary is difficult to extend to the central region due to the restricted change of particle contact conditions.

The packing of cohesive particles is of paramount importance in many industries because the packing structure is closely related to process performance. A general relation between packing density and interparticle force was previously proposed based on packing structures formed without dynamic fluid flows. Its universality is examined here in two different packings, formed in settling and defluidization of static and dynamic fluids, respectively. First, it is shown that the packings of the same particles formed by two different methods have different structures because of different impact-induced pressures. Nevertheless, a one-to-one relationship between packing density and structural properties still holds regardless of the different packing methods, and the force distribution in those packings obeys similar rules. Finally, the packing densities obtained by the different methods are demonstrated to be universally correlated with the ratio of the interparticle force to the effective gravity. These findings indicate that different phenomena of particulate systems at a macro- or meso-scale may share similar microscopic origins, with the interparticle force playing a crucial role.

Discrete particle simulation can explicitly consider interparticle forces and obtain microscopic properties of the fluidized cohesive particles, but it is computationally expensive. It is thus pivotal to link the microscopic discrete properties to the macroscopic continuum description of the system for large scale applications. This work studies the fluidization of cohesive particles through the coupled computational fluid dynamics and discrete element method (CFD-DEM). First, discrete CFD-DEM results show the increased particle cohesion leads to the severe particle agglomeration which affects the fluidization quality significantly. Then, continuum properties are attained by a weighted time-volume averaging method, showing that tensile pressure becomes significant as particle cohesion increases. By incorporating Rumpf correlation into the solid pressure equation, the tensile pressure could be predicted consistently with the averaged CFD-DEM results for different particle cohesion. Finally, those overall steady averaged properties of the bed are obtained for understanding the general macroscopic properties of the system.

To identify the dense packing of cylinder–sphere binary mixtures (spheres as filling objects), the densification process of such binary mixtures subjected to three-dimensional (3D) mechanical vibrations was experimentally studied. Various influential factors including vibration parameters (such as vibration time t, vibration amplitude A, frequency ω, vibration acceleration Γ) as well as particle size ratio r (small sphere vs. large cylinder), composition of the binary mixtures X_L (volume fraction of cylinders), and container size D (container diameter) on the packing density ρ were systematically investigated. The results show that the optimal vibration parameters for different binary cylinder–sphere mixtures are different. The smaller the size ratio, the less vibration acceleration is needed to form a stable dense packing. For each binary mixture, high packing density can be obtained when the volume fraction of large cylindrical particles is dominant. Meanwhile, increasing the container size can decrease the container wall effect and get higher packing density. The proposed analytical model has been proved to be valid in predicting the packing densification of current cylinder–sphere binary mixtures.

In this paper, the transition from random to ordered packings of mono-sized cylindrical particles under 3D mechanical vibration was simulated by discrete element method (DEM). The effects of particle aspect ratio, size of the particulate system and container wall on the granular crystallization were investigated. And the mechanisms were analyzed through the characterization of the order transition process in terms of packing density, coordination number (CN), orientational ordering parameter (O), nucleation and growth of cluster and granular temperature (θ). The results show that nearly perfect crystallization of mono-sized cylindrical particles can be achieved with specific aspect ratio and proper vibration conditions in a cylindrical container. The orientational ordering parameter demonstrates that the crystallization firstly starts from the container wall and then propagates inward gradually. The lower granular temperature in a cuboid container indicates less vibration energy transferred to the granular assembly compared with that in a cylindrical container, illustrating the critical role of container shape in crystallization. The vibrated crystallization of mono-sized cylindrical particles is analogous to entropy-driven process, which can be gradually achieved by the self-assembly of particles with parallel alignments along the already formed ordered clusters (nuclei)or the container wall. These results can help design complex and ordered granular structures.

Understanding the relationship between a fluid flow and the structural properties of a bed is important for various industrial applications and a proper description of particle-fluid flow. This work presents a pore-scale study of fluid flow through randomly packed beds by a network model. The model incorporates the inertial effect and thus can be applied to flows of high Reynolds numbers. The results show the structure heterogeneity associated with the connection of pores is important in determining the distribution of fluid flow. The statistical distribution of normalized drag forces on individual particles is Gaussian, related to the statistical distribution of pore properties. The mean drag force of a bed by the pore-scale model agrees well with that from a previous study by the lattice-Boltzmann method. These findings support the application of the pore network model for simulating particle-fluid flows under a wider range of Reynolds numbers.

The dynamic crystallization of cubic granular particles under three-dimensional mechanical vibration is numerically investigated by the discrete element method. The effects of operational conditions (vibration, container shape and system size) and particle properties (gravity and friction) on the formation of crystals and defects are discussed. The results show that the formation and growth of clusters with face-to-face aligned cubic particles can be easily realized under vibrations. Especially, a single crystal with both translational and orientational ordering can be reproduced in a rectangular container under appropriate vibrations. It is also found that the gravitational effect is beneficial for the ordering of a packing; the ordering of frictional particles can be improved significantly with an enlarged gravitational acceleration. The flat walls of a rectangular container facilitate the formation of orderly layered structures. The curved walls of a cylindrical container contribute to the formation of ring-like structures, whereas they also cause distortions and defects in the packing centers. Finally, it is shown that the crystallization of inelastic particles is basically accomplished by the pursuit of a better mechanical stability of the system, with decreasing kinetic and potential energies.

The packing densification of mono-sized equilateral cylindrical particles under mechanical vibration is numerically reproduced using discrete element method (DEM). The influences of vibration frequency, amplitude and container size on the macro property (e.g. packing density) of each packing are studied. Meanwhile, various micro-properties including coordination number (CN), radial distribution function (RDF), local structures, contact types, particle position/orientation distributions, forces/stresses of the vibrated dense packing are characterized and compared with those of the loose initial poured packing. The results show that properly controlling vibration conditions can realize the transition of equilateral cylindrical particles from random loose packing (RLP) to random close packing (RCP). The maximum packing density without wall effects can reach about 0.7166, which agrees with experimental and numerical results in literature. Micro property analyses demonstrate that the average CN increases slightly after vibration. The RDF curves indicate three obvious peaks for both poured and vibrated packings. The distributions of intersection angles imply that the perpendicular arrangements of the cylindrical particles are common in both packing structures. From RLP to RCP, the probability of side-edge, bottom-edge and edge-edge contacts between two particles decreases, while that of side-side, side-bottom and bottom-bottom contacts increases. Both particle position and orientation distributions illustrate that the structure in the center of the vibrated packing is disordered. The distribution of strong forces follows the exponential law, while that of weak forces follows the power law. The static vertical stresses in both packings can be predicted by Janssen model. After vibration, a much denser and more stable structure with a larger saturation stress is obtained due to the reducing inter-particle friction effects.

This paper presents a systematic numerical investigation of static stress profile within a confined granular packing using discrete element method. The vertical and horizontal stress profiles are carefully identified within the packing structure, and the effects of container diameter and friction coefficient on the stress distributions are systematically investigated and analyzed. The results show a quantitative agreement between the vertical stress profile gauged at the bottom and the stress profile calculated within the packing structure. I.e. beyond a hydrostatic region, the static vertical stresses saturate exponentially with the packing depth. A positive correlation between the saturation stress and the container size and a negative correlation with the friction coefficient can be observed. Besides, it is also found that the well-known Janssen coefficient (or Janssen constant) is not a constant value; it decreases asymptotically to a constant with the packing depth, which implies a non-constant friction effects existed between the granular assemblies and the boundaries. And the analysis of contact forces within the packing structure also indicates a stabilized condition beyond the hydrostatic region. It is believed that these findings could develop a comprehensive insight on the stress distribution of granular matter.

Bed structure is important to heat and mass transfer in fluidization. This study investigates solid structural transition for cohesive particles by the combined approach of computational fluid dynamics and discrete element method, supported by Voronoi tessellation. Macroscopic behaviors of fluidized beds are first discussed in connection with microscopic structural transitions. Then, the properties of Voronoi polyhedra are analyzed at both bed and particle scales. In addition, the correlation of coordination number and porosity is examined at a particle scale, and their combined probability distribution is analyzed to identify dominant structure of particles in different flow regimes. Finally, an index is proposed as the ratio of coordination number and porosity to differentiate microscopic states of a particle. These findings should be useful for the study of flow, heat, and mass transfer in fluidized beds and for the understanding of solid-like to fluid-like transition of granular materials.

Packing densification of cubical particles under mechanical vibrations was dynamically simulated by using discrete element method (DEM). Effects of operating parameters such as vibration amplitude, frequency, vibration intensity, and container size (container wall) on packing densification were comprehensively investigated. The macro property such as packing density and micro properties such as coordination number (CN), radial distribution function (RDF), and particle orientation of the packings were analyzed and compared. It is found that mechanical vibration with proper vibration amplitude and frequency is effective for the densification of cubical particle packing. Packing structures of different packing densities display different properties, based on which random loose packing (RLP) and random close packing (RCP) of cubical particles are identified with the packing density of 0.591 and 0.683, respectively. Two densification mechanisms are discussed as the particle rearrangement is dominant for the transition from RLP to RCP and the crystallization along the container wall is dominant for the transition beyond RCP to ordering. The obtained results are useful for optimizing vibration conditions to generate dense packings and understanding the structural information of some fixed beds with cubical particles.

Densification of cubic particles under three-dimensional (3D) mechanical vibration was studied experimentally. Effects of vibration time (t), frequency (f), vibration amplitude (A), vibration acceleration (Г), container size (D) and particle sphericity (φ) on packing density (ρ) were comprehensively analyzed. To identify the effects of particle shape, the packing densification of cuboid 1 (12 mm × 12 mm × 28 mm) and cuboid 2 (4 mm × 8 mm × 16 mm) were systematically studied under the same conditions. The results show that the structure of cubic particles can be first densified from random loose packing (RLP) to random close packing (RCP) and then to ordered packing (OP) gradually. In comparison, cuboid 1 and cuboid 2 particles can only form RCP structure, but cannot achieve OP even under further vibration. Vibration parameters (t, f, A and Г) are shown to be important to the packing densification. Based on the results of varying f and A, A - f phase diagrams are established for choosing the optimal vibration parameters to achieve the desired dense packing structures. Besides, it is shown the size of container (wall effect) has monotonic influence on packing density, i.e., the larger container size corresponds to the less wall effect and higher packing density. Cubic particles can form ordered packing because of the geometrical symmetry with aspect ratio of 1. After eliminating the wall effect by extrapolating the packing densities in different sized containers, typical packing densities of the three types of particles are obtained with ρ_RLP = 0.658, ρ_RCP = 0.830 and ρ_OP = 0.965 for cubic particles; ρ_RLP = 0.625 and ρ_RCP = 0.740 for cuboid 1 particles; ρ_RLP = 0.591 and ρ_RCP = 0.731 for cuboid 2 particles. These findings indicate cubic particles are efficient in densification which can be readily realized through proper 3D mechanical vibration.

Systematic physical experiments examining the packing densification of mono-sized cylindrical particles subject to 3D mechanical vibration were carried out. The influence of vibration conditions such as vibration time, frequency, amplitude, vibration strength, container size, and the aspect ratio and sphericity of the particle on the packing density were analyzed and discussed. For each initial packing density with a certain aspect ratio, operating parameters were optimized to achieve much denser packing. The results indicate that the packing density initially increases with vibration time and then remains constant. The effects of vibration frequency and amplitude on the packing densification have similar trends, i.e. the packing density first increases with the vibration frequency or amplitude to a high value and then decreases; too large or small frequency or amplitude does not enhance densification. Increasing the container size can reduce container wall effects and help achieve a high packing density. Varying the particle aspect ratio and sphericity can lead to different dense random packing structures. Overall, based on results of the examined systems, the highest random packing density obtained in an infinite sized container can reach 0.73, which agrees well with corresponding numerical and analytical results in the literature.

The packing densification of mono-sized spheres under compression is numerically modelled and studied by using the discrete element method (DEM). The obtained macro packing property such as packing density and micro properties such as coordination number (CN), radial distribution function (RDF), angular distribution function (ADF), and pore structure (Voronoi Delaunay tessellation) are characterised and compared with those properties of random loose packing (RLP) obtained under natural packing and random close packing (RCP) obtained under one-dimensional (1D) vibration. The results indicate that by properly controlling the pressure, the maximum random packing density of about 0·64 can be realised, implying that external compression is an effective way to realise the transition from RLP to RCP. Besides, the properties of RCP obtained under compression in this study are much comparable with that obtained under 1D vibration. The pushing filling mechanism of macro pores under compression was also identified by dynamic analysis of the densification process.